While sine (read the story of the word sine) was named after mathematicians who wrote in Arabic, the name of cosine was coined by Europeans who wrote in Latin. From the history of sine it is clear that the name sinus It was not best suited to represent this mathematical concept. However, as it was used by most mathematicians of the time, the cosine was eventually based on it as well, as there was a need to express the "complement" of sine.
From the fifteenth century, when the term cosine did not exist, some mathematicians began to use other expressions to define it, such as sinus rectus complementi (Regiomontanus), sinus rectus secundus / sinus residuae (Vieta) and sinus secundus (Magini)
The term co.sinus first appears in the work Canon triangulorum (1620), by Edmund Gunter, English mathematician of Welsh descent. In this paper, the cosine (co.sinus) is defined as an abbreviation for sinus complementi (sine of complementary angle). A little later, in 1658, this term would have been modified by John Newton to cosinus, this format being accepted and used by all.
The Oxford Dictionary contains the English form (cosine) in a passage from 1635:As the Radius Is the cosine of the angle given”(As the radius is for the cosine of the given angle).